If I am rendering with blender, can I open a new project while it is rendering?
Just open a new instance of Blender:

Windows:
Right click on the blender icon then choose Blender. This will open new blender instance.

Linux:
Just run the application another time

Mac OS:
By default, only 1 instance of an app can be run. You can work around this limitation by invoking Blender from the terminal command line. open -n /Applications/blender.app